Q: Step 1: Normalize RGB values.

$R = 75 \div 255 = 0.2941$ $G = 150 \div 255 = 0.5882$ $B = 225 \div 255 = 0.8824$

Q: Step 2: Find $C_{max}$, $C_{min}$, and $\Delta$.

$C_{max} = 0.8824$ (which is Blue) $C_{min} = 0.2941$ (which is Red) $\Delta = 0.8824 - 0.2941 = 0.5883$

Q: Step 3: Calculate Lightness (L).

$L = \frac{0.8824 + 0.2941}{2} = \frac{1.1765}{2} = 0.58825$ Expressed as a percentage, Lightness = 58.8%.

Q: Step 4: Calculate Saturation (S).

$S = \frac{0.5883}{1 - |2 \times 0.58825 - 1|}$ $S = \frac{0.5883}{1 - |1.1765 - 1|}$ $S = \frac{0.5883}{1 - 0.1765} = \frac{0.5883}{0.8235} = 0.7144$ Expressed as a percentage, Saturation = 71.4%.

Q: Step 5: Calculate Hue (H).

Since $C_{max}$ is Blue ($0.8824$), we use the third Hue formula: $H = 60^\circ \times (\frac{0.2941 - 0.5882}{0.5883} + 4)$ $H = 60^\circ \times (\frac{-0.2941}{0.5883} + 4)$ $H = 60^\circ \times (-0.5 + 4)$ $H = 60^\circ \times 3.5 = 210^\circ$

Q: 1. Calculate Key (Black):

$K = 1 - \max(R, G, B)$ If $K = 1$ (meaning $R=0, G=0, B=0$), then $C = 0, M = 0, Y = 0$, and the calculation is complete.

Q: 2. Calculate Cyan, Magenta, and Yellow:

$C = \frac{1 - R - K}{1 - K}$ $M = \frac{1 - G - K}{1 - K}$ $Y = \frac{1 - B - K}{1 - K}$

Question 1

1. Lightness (L):

Accepted Answer

$L = \frac{C_{max} + C_{min}}{2}$

Question 2

2. Saturation (S):

Accepted Answer

If $\Delta = 0$ (the color is a shade of gray), then $S = 0$.
If $\Delta 
eq 0$, then $S = \frac{\Delta}{1 - |2L - 1|}$

Question 3

3. Hue (H):

Accepted Answer

If $\Delta = 0$, $H = 0^\circ$.
If $C_{max} = R$, $H = 60^\circ 	imes (\frac{G - B}{\Delta} \mod 6)$.
If $C_{max} = G$, $H = 60^\circ 	imes (\frac{B - R}{\Delta} + 2)$.
If $C_{max} = B$, $H = 60^\circ 	imes (\frac{R - G}{\Delta} + 4)$.
If $H < 0^\circ$, add $360^\circ$ to normalize it.

Question 4

Step 1: Normalize RGB values.

Accepted Answer

$R = 75 \div 255 = 0.2941$
$G = 150 \div 255 = 0.5882$
$B = 225 \div 255 = 0.8824$

Question 5

Step 2: Find $C_{max}$, $C_{min}$, and $\Delta$.

Accepted Answer

$C_{max} = 0.8824$ (which is Blue)
$C_{min} = 0.2941$ (which is Red)
$\Delta = 0.8824 - 0.2941 = 0.5883$

Question 6

Step 3: Calculate Lightness (L).

Accepted Answer

$L = \frac{0.8824 + 0.2941}{2} = \frac{1.1765}{2} = 0.58825$
Expressed as a percentage, Lightness = 58.8%.

Question 7

Step 4: Calculate Saturation (S).

Accepted Answer

$S = \frac{0.5883}{1 - |2 	imes 0.58825 - 1|}$
$S = \frac{0.5883}{1 - |1.1765 - 1|}$
$S = \frac{0.5883}{1 - 0.1765} = \frac{0.5883}{0.8235} = 0.7144$
Expressed as a percentage, Saturation = 71.4%.

Question 8

Step 5: Calculate Hue (H).

Accepted Answer

Since $C_{max}$ is Blue ($0.8824$), we use the third Hue formula:
$H = 60^\circ 	imes (\frac{0.2941 - 0.5882}{0.5883} + 4)$
$H = 60^\circ 	imes (\frac{-0.2941}{0.5883} + 4)$
$H = 60^\circ 	imes (-0.5 + 4)$
$H = 60^\circ 	imes 3.5 = 210^\circ$

Question 9

1. Calculate Key (Black):

Accepted Answer

$K = 1 - \max(R, G, B)$
If $K = 1$ (meaning $R=0, G=0, B=0$), then $C = 0, M = 0, Y = 0$, and the calculation is complete.

Question 10

2. Calculate Cyan, Magenta, and Yellow:

Accepted Answer

$C = \frac{1 - R - K}{1 - K}$
$M = \frac{1 - G - K}{1 - K}$
$Y = \frac{1 - B - K}{1 - K}$

Question 11

Step 1: Normalize RGB values.

Accepted Answer

$R = 200 \div 255 = 0.7843$
$G = 100 \div 255 = 0.3922$
$B = 50 \div 255 = 0.1961$

Question 12

Step 2: Calculate Key (K).

Accepted Answer

The maximum normalized value is $R$ ($0.7843$).
$K = 1 - 0.7843 = 0.2157$
Expressed as a percentage, K = 21.6%.

Question 13

Step 3: Calculate Cyan (C).

Accepted Answer

$C = \frac{1 - 0.7843 - 0.2157}{1 - 0.2157}$
$C = \frac{0}{0.7843} = 0$
Expressed as a percentage, C = 0%. (This makes logical sense; Cyan absorbs Red light. Because the Red channel is the dominant color in this orange, we want zero Cyan ink so that all Red light is reflected).

Question 14

Step 4: Calculate Magenta (M).

Accepted Answer

$M = \frac{1 - 0.3922 - 0.2157}{1 - 0.2157}$
$M = \frac{0.3921}{0.7843} = 0.5000$
Expressed as a percentage, M = 50.0%.

Question 15

Step 5: Calculate Yellow (Y).

Accepted Answer

$Y = \frac{1 - 0.1961 - 0.2157}{1 - 0.2157}$
$Y = \frac{0.5882}{0.7843} = 0.7500$
Expressed as a percentage, Y = 75.0%.

Question 16

Phase 1: Inverse Gamma Correction.

Accepted Answer

Let $R, G, B$ be normalized [0, 1]. For each channel (represented by $v$):
If $v \leq 0.04045$, then $v_{linear} = \frac{v}{12.92}$
If $v > 0.04045$, then $v_{linear} = (\frac{v + 0.055}{1.055})^{2.4}$

Question 17

Phase 2: Matrix Multiplication (sRGB to XYZ with D65 illuminant).

Accepted Answer

$X = (v_R 	imes 0.4124) + (v_G 	imes 0.3576) + (v_B 	imes 0.1805)$
$Y = (v_R 	imes 0.2126) + (v_G 	imes 0.7152) + (v_B 	imes 0.0722)$
$Z = (v_R 	imes 0.0193) + (v_G 	imes 0.1192) + (v_B 	imes 0.9505)$

Question 18

Phase 3: XYZ to LAB.

Accepted Answer

Let $X_n = 0.95047, Y_n = 1.00000, Z_n = 1.08883$ (the D65 reference white values).
Calculate $t_x = \frac{X}{X_n}$, $t_y = \frac{Y}{Y_n}$, $t_z = \frac{Z}{Z_n}$.
Apply the transformation function $f(t)$ to each:
If $t > 0.008856$, $f(t) = t^{1/3}$
If $t \leq 0.008856$, $f(t) = (7.787 	imes t) + \frac{16}{116}$

Question 19

Step 1: Normalize and Linearize.

Accepted Answer

$R = 1.0, G = 0.0, B = 0.0$.
Since $1.0 > 0.04045$, $v_R = (\frac{1.0 + 0.055}{1.055})^{2.4} = 1.0$.
Since $0.0 \leq 0.04045$, $v_G = 0.0$, $v_B = 0.0$.

Question 20

Step 2: Calculate XYZ.

Accepted Answer

$X = (1.0 	imes 0.4124) + 0 + 0 = 0.4124$
$Y = (1.0 	imes 0.2126) + 0 + 0 = 0.2126$
$Z = (1.0 	imes 0.0193) + 0 + 0 = 0.0193$

Question 21

Step 3: Transform to LAB.

Accepted Answer

$t_x = \frac{0.4124}{0.95047} = 0.4338$
$t_y = \frac{0.2126}{1.00000} = 0.2126$
$t_z = \frac{0.0193}{1.08883} = 0.0177$

Question 22

What is the difference between HEX and RGB?

Accepted Answer

HEX (Hexadecimal) and RGB are not different color spaces; they are simply different numerical formats for the exact same RGB color model. RGB expresses the red, green, and blue values in base-10 decimal numbers (from 0 to 255). HEX expresses those exact same values in base-16 alphanumeric code (from 00 to FF). For example, pure red is (255, 0, 0) in RGB and #FF0000 in HEX. They produce the exact same color on a screen and require no complex mathematical conversion other than a base number translation.

Question 23

Why do my vibrant digital colors look dull when printed?

Accepted Answer

Digital screens emit light (RGB), allowing them to produce highly saturated, neon, and luminescent colors. Printers use ink (CMYK) to absorb light, which inherently limits the saturation they can achieve. The gamut (range of color) of CMYK is physically much smaller than RGB. When a color space converter translates your digital file for print, it must clip those vibrant out-of-gamut colors to the nearest printable duller shade.

Question 24

Is it possible to convert CMYK back to RGB without losing quality?

Accepted Answer

No, it is not possible. Converting from a wider color space (RGB) to a narrower one (CMYK) permanently discards the color data that falls outside the CMYK gamut. If you convert that CMYK file back to RGB, the software cannot magically guess what the original vibrant colors were; it simply translates the dull CMYK colors into dull RGB equivalents. This is why designers must always keep a master copy of their work in RGB.

Question 25

What is an ICC Profile and why do I need it?

Accepted Answer

An ICC (International Color Consortium) profile is a standardized digital file containing data that characterizes a color input or output device. It acts as a customized dictionary for a color space converter. Instead of using generic math, the converter uses the ICC profile to understand exactly how your specific monitor displays red, or how a specific printing press prints cyan, ensuring the translation between devices is physically accurate.

Question 26

Which RGB color space should I use for web design?

Accepted Answer

You should strictly use sRGB for standard web design. Almost all web browsers, mobile phones, and consumer monitors are calibrated to assume untagged web graphics are in the sRGB color space. If you design a website using a wider gamut like Adobe RGB and upload it without proper color profile tagging, the user's browser will misinterpret the numbers, resulting in colors that look washed out and incorrect.

Question 27

What is rendering intent in color conversion?

Accepted Answer

Rendering intent is the specific rule a color space converter follows when it encounters a color in the original file that cannot be reproduced in the destination space (an out-of-gamut color). The two most common are "Perceptual," which compresses all colors to maintain their visual relationships (best for photos), and "Relative Colorimetric," which matches printable colors exactly but flattens unprintable colors to the closest match (best for logos and vector graphics).

Question 28

Why is the math for converting to CIE LAB so complicated?

Accepted Answer

Unlike RGB or CMYK, which map physical hardware outputs, CIE LAB is a mathematical model of human biological vision. Human vision is highly non-linear; we are more sensitive to changes in dark colors than bright colors, and more sensitive to green wavelengths than blue. The complex matrices and cube-root transformations required to convert RGB to LAB are necessary to accurately model these biological quirks and map colors to a perceptually uniform 3D space.

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